Package 'BEND'

Bayesian Bivariate Piecewise Random Effects Model (BPREM)

Description

Estimates a Bayesian bivariate piecewise random effects models (BPREM) for longitudinal data with two interrelated outcomes. See Peralta et al. (2022) for more details.

Usage

Bayes_BPREM(
  data,
  id_var,
  time_var,
  y1_var,
  y2_var,
  iters_adapt = 5000,
  iters_burn_in = 1e+05,
  iters_sampling = 50000,
  thin = 15,
  save_full_chains = FALSE,
  save_conv_chains = FALSE,
  verbose = TRUE
)

Arguments

data	Data frame in long format, where each row describes a measurement occasion for a given individual. It is assumed that each individual has the same number of assigned timepoints (a.k.a., rows). There can be missingness in the outcomes (y1_var and y2_var), but there cannot be missingness in time (time_var).
id_var	Name of column that contains ids for individuals with repeated measures in a longitudinal dataset.
time_var	Name of column that contains the time variable. This column cannot contain any missing values.
y1_var	Name of column that contains the first outcome variable. Missing values should be denoted by NA.
y2_var	Name of column that contains the second outcome variable. Missing values should be denoted by NA.
iters_adapt	(optional) Number of iterations for adaptation of jags model (default = 5000).
iters_burn_in	(optional) Number of iterations for burn-in (default = 100000).
iters_sampling	(optional) Number of iterations for posterior sampling (default = 50000).
thin	(optional) Thinning interval for posterior sampling (default = 15).
save_full_chains	Logical indicating whether the MCMC chains from rjags should be saved (default = FALSE). Note, this should not be used regularly as it will result in an object with a large file size.
save_conv_chains	Logical indicating whether the MCMC chains from rjags should be saved but only for the parameters monitored for convergence (default = FALSE). This would be useful for plotting traceplots for relevant model parameters to evaluate convergence behavior. Note, this should not be used regularly as it will result in an object with a large file size.
verbose	Logical controlling whether progress messages/bars are generated (default = TRUE).

Details

For more information on the model equation and priors implemented in this function, see Peralta et al. (2022).

Value

A list (an object of class BPREM) with elements:

Call	A list of all specified function arguments.
Sample Size	Number of subjects (n_subj) and number of timepoints (n_time) in the dataset.
Data	Dataset used for estimation.
Convergence	Potential scale reduction factor (PSRF) for each parameter (parameter_psrf), Gelman multivariate scale reduction factor (multivariate_psrf), and mean PSRF (mean_psrf) to assess model convergence.
Model_Fit	Deviance (deviance), effective number of parameters (pD), and Deviance information criterion (dic) to assess model fit.
Fitted_Values	Data frame with the fitted values for y1 and y2 at each timepoint for each individual.
Parameter_Estimates	Data frame with posterior mean and 95% credible intervals for each model parameter.
Random_Coefficients	List object with data frames providing random effects and random coefficients for each individual.
Run_Time	Total run time for model fitting.
Full_MCMC_Chains	If save_full_chains=TRUE, raw MCMC chains from rjags.
Convergence_MCMC_Chains	If save_conv_chains=TRUE, raw MCMC chains from rjags but only for the parameters monitored for convergence.

Author(s)

Corissa T. Rohloff, Yadira Peralta

References

Peralta, Y., Kohli, N., Lock, E. F., & Davison, M. L. (2022). Bayesian modeling of associations in bivariate piecewise linear mixed-effects models. Psychological Methods, 27(1), 44–64. https://doi.org/10.1037/met0000358

Examples

# load simulated data
data(SimData_BPREM)
# fit Bayes_BPREM()
results_bprem <- Bayes_BPREM(data = SimData_BPREM,
                             id_var = "id",
                             time_var = "time",
                             y1_var = "y1",
                             y2_var = "y2")
# result summary
summary(results_bprem)
# plot fitted results
plot(results_bprem)

---

Bayesian Crossed Random Effects Model (CREM)

Description

Estimates a Bayesian crossed random effects models (CREM) for longitudinal data with dynamic group membership. Four different choices for functional forms are provided: linear, quadratic, exponential, and piecewise. See Rohloff et al. (2024) for more details.

Usage

Bayes_CREM(
  data,
  ind_id_var,
  cross_id_var,
  time_var,
  y_var,
  form = "linear",
  fixed_effects = NULL,
  iters_adapt = 5000,
  iters_burn_in = 50000,
  iters_sampling = 50000,
  thin = 15,
  save_full_chains = FALSE,
  save_conv_chains = FALSE,
  verbose = TRUE
)

Arguments

data	Data frame in long format, where each row describes a measurement occasion for a given individual. It is assumed that each individual has the same number of assigned timepoints (a.k.a., rows). There can be missingness in the outcome (y_var), but there cannot be missingness in time (time_var).
ind_id_var	Name of column that contains ids for individuals with repeated measures in a longitudinal dataset (e.g., students).
cross_id_var	Name of column that contains ids for the crossed factor (e.g., teachers).
time_var	Name of column that contains the time variable. This column cannot contain any missing values.
y_var	Name of column that contains the outcome variable. Missing values should be denoted by NA.
form	Name of the functional form. Options include: ‘linear’ (default), ‘quadratic’, ‘exponential’, ‘piecewise’.
fixed_effects	(optional) Starting values for the fixed effects parameters.
iters_adapt	(optional) Number of iterations for adaptation of jags model (default = 5000).
iters_burn_in	(optional) Number of iterations for burn-in (default = 50000).
iters_sampling	(optional) Number of iterations for posterior sampling (default = 50000).
thin	(optional) Thinning interval for posterior sampling (default = 15).
save_full_chains	Logical indicating whether the MCMC chains from rjags should be saved (default = FALSE). Note, this should not be used regularly as it will result in an object with a large file size.
save_conv_chains	Logical indicating whether the MCMC chains from rjags should be saved but only for the parameters monitored for convergence (default = FALSE). This would be useful for plotting traceplots for relevant model parameters to evaluate convergence behavior. Note, this should not be used regularly as it will result in an object with a large file size.
verbose	Logical controlling whether progress messages/bars are generated (default = TRUE).

Details

For more information on the model equation and priors implemented in this function, see Rohloff et al. (2024).

Note, this function differs from the above reference by estimating the covariances between the random effects parameters. The variance-covariance matrices of the individual and group random effects have a scaled inverse-Wishart prior (see Peralta et al., 2022).

Value

A list (an object of class CREM) with elements:

Call	A list of all specified function arguments.
Sample Size	Number of subjects (n_subj), number of groups (n_group) and number of timepoints (n_time) in the dataset.
Data	Dataset used for estimation.
Convergence	Potential scale reduction factor (PSRF) for each parameter (parameter_psrf), Gelman multivariate scale reduction factor (multivariate_psrf), and mean PSRF (mean_psrf) to assess model convergence.
Model_Fit	Deviance (deviance), effective number of parameters (pD), and Deviance information criterion (dic) to assess model fit.
Fitted_Values	Data frame with the fitted values at each timepoint for each individual.
Functional_Form	Functional form fitted.
Parameter_Estimates	Data frame with posterior mean and 95% credible intervals for each model parameter.
Random_Coefficients	List object with data frames providing individual random effects, group random effects, and random coefficients for each individual and group.
Run_Time	Total run time for model fitting.
Full_MCMC_Chains	If save_full_chains=TRUE, raw MCMC chains from rjags.
Convergence_MCMC_Chains	If save_conv_chains=TRUE, raw MCMC chains from rjags but only for the parameters monitored for convergence.

Author(s)

Corissa T. Rohloff

References

Peralta, Y., Kohli, N., Lock, E. F., & Davison, M. L. (2022). Bayesian modeling of associations in bivariate piecewise linear mixed-effects models. Psychological Methods, 27(1), 44–64. https://doi.org/10.1037/met0000358

Rohloff, C. T., Kohli, N., & Lock, E. F. (2024). Identifiability and estimability of Bayesian linear and nonlinear crossed random effects models. British Journal of Mathematical and Statistical Psychology. https://doi.org/10.1111/bmsp.12334

Examples

# load simulated data
data(SimData_PCREM)
# fit Bayes_CREM()
results_pcrem <- Bayes_CREM(data = SimData_PCREM,
                            ind_id_var = "id",
                            cross_id_var = "teacherid",
                            time_var = "time",
                            y_var = "y",
                            form="piecewise")
# result summary
summary(results_pcrem)
# plot fitted results
plot(results_pcrem)

---

Bayesian Piecewise Random Effects Model (PREM) + Extensions

Description

Estimates a Bayesian piecewise random effects model (PREM), with some useful extensions. There are three model options included in this function:

• PREM estimates a Bayesian piecewise random effects model with a latent number of changepoints (default). Allows the inclusion of outcome-predictive covariates (CI-PREM).

• PREMM estimates a piecewise random effects mixture model for a given number of latent classes and a latent number of possible changepoints in each class.

• CI-PREMM estimates a covariate influenced piecewise random effects mixture model for a given number of latent classes and a latent number of possible changepoints in each class. Allows the inclusion of outcome- and/or class-predictive covariates. See Lock et al. (2018) and Lamm (2022) for more details.

Usage

Bayes_PREM(
  data,
  id_var,
  time_var,
  y_var,
  n_class = 1,
  max_cp = 2,
  class_predictive_vars = NULL,
  outcome_predictive_vars = NULL,
  scale_prior = "uniform",
  alpha = 1,
  cp_prior = "binomial",
  binom_prob = 0.5,
  iters_adapt = 1000,
  iters_burn_in = 20000,
  iters_sampling = 30000,
  thin = 15,
  save_full_chains = FALSE,
  save_conv_chains = FALSE,
  verbose = TRUE
)

Arguments

data	Data frame in long format, where each row describes a measurement occasion for a given individual. It is assumed that each individual has the same number of assigned timepoints (a.k.a., rows). There can be missingness in the outcome (y_var), but there cannot be missingness in time (time_var).
id_var	Name of column that contains ids for individuals with repeated measures in a longitudinal dataset.
time_var	Name of column that contains the time variable. This column cannot contain any missing values.
y_var	Name of column that contains the outcome variable. Missing values should be denoted by NA.
n_class	Number of latent classes (default = 1). Note, CI-PREMM only allows for two classes.
max_cp	Maximum number of changepoints in each latent class (default = 2).
class_predictive_vars	Name(s) of column(s) that contain class-predictive covariates (time-invariant only). Give a vector of names if multiple covariates. Note, there cannot be any missingness in the covariates.
outcome_predictive_vars	Name(s) of column(s) that contain outcome-predictive covariates (time-varying or -invariant). Give a vector of names if multiple covariates. Note, there cannot be any missingness in the covariates.
scale_prior	Prior for the scale parameter for the hierarchical random effects. Options include: ‘uniform’ (scaled uniform prior; default) or ‘hc’ (scaled half-cauchy prior).
alpha	Concentration parameter for Dirichlet prior for latent classes (default = 1). This can be a vector of values corresponding to the number of classes (specified by n_class). Note, this is not used for CI-PGMM.
cp_prior	Prior for the number of changepoints in each class. Options include: 'binomial' (default) or 'uniform'.
binom_prob	Probability for binomial prior, if specified (default = 0.5).
iters_adapt	(optional) Number of iterations for adaptation of jags model (default = 1000).
iters_burn_in	(optional) Number of iterations for burn-in (default = 20000).
iters_sampling	(optional) Number of iterations for posterior sampling (default = 30000).
thin	(optional) Thinning interval for posterior sampling (default = 15).
save_full_chains	Logical indicating whether the MCMC chains from rjags should be saved (default = FALSE). Note, this should not be used regularly as it will result in an object with a large file size.
save_conv_chains	Logical indicating whether the MCMC chains from rjags should be saved but only for the parameters monitored for convergence (default = FALSE). This would be useful for plotting traceplots for relevant model parameters to evaluate convergence behavior. Note, this should not be used regularly as it will result in an object with a large file size.
verbose	Logical controlling whether progress messages/bars are generated (default = TRUE).

Details

For more information on the model equation and priors implemented in this function, see Lamm et al. (2022; CI-PREMM) and Lock et al. (2018; PREMM).

Value

A list (an object of class PREM) with elements:

Call	A list of all specified function arguments.
Sample Size	Number of subjects (n_subj) and number of timepoints (n_time) in the dataset.
Data	Dataset used for estimation.
Convergence	Potential scale reduction factor (PSRF) for each parameter (parameter_psrf), Gelman multivariate scale reduction factor (multivariate_psrf), and mean PSRF (mean_psrf) to assess model convergence.
Model_Fit	Deviance (deviance), effective number of parameters (pD), and Deviance information criterion (dic) to assess model fit.
Fitted_Values	Data frame with the fitted values at each timepoint for each individual.
Parameter_Estimates	Data frame with posterior mean and 95% credible intervals for each model parameter.
Random_Coefficients	List object with data frames providing random coefficients for each individual.
Run_Time	Total run time for model fitting.
Full_MCMC_Chains	If save_full_chains=TRUE, raw MCMC chains from rjags.
Convergence_MCMC_Chains	If save_conv_chains=TRUE, raw MCMC chains from rjags but only for the parameters monitored for convergence.

Class_Information contains a list with elements:

class_membership	Vector of length n with class membership assignments for each individual.
individ_class_probability	nxC matrix with each individual’s probabilities of belonging to each class conditional on their class-predictive covariates (when applicable) and growth curve.
unconditional_class_probability	This output will differ based on which model was fit. For a PREM or CI-PREM, this will equal 1 as there is only one class. For a PREMM or CI-PREMM with only outcome-predictive covariates, this will be a vector of length C denoting the population probability of belonging to each class. For a CI-PREMM with class-predictive covariates, this will be a vector of length n denoting the probability of each individual belonging to the non-reference class (Class 2) based on their class-predictive covariates only.

Author(s)

Corissa T. Rohloff, Rik Lamm, Eric F. Lock

References

Lamm, R. (2022). Incorporation of covariates in Bayesian piecewise growth mixture models. https://hdl.handle.net/11299/252533

Lock, E. F., Kohli, N., & Bose, M. (2018). Detecting multiple random changepoints in Bayesian piecewise growth mixture models. Psychometrika, 83(3), 733–750. https://doi.org/10.1007/s11336-017-9594-5

Examples

# load simulated data
data(SimData_PREM)

# PREM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_prem <- Bayes_PREM(data = SimData_PREM,
                           id_var = "id",
                           time_var = "time",
                           y_var = "y")
# result summary
summary(results_prem)
# plot fitted results
plot(results_prem)

# CI-PREM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_ciprem <- Bayes_PREM(data = SimData_PREM,
                             id_var = "id",
                             time_var = "time",
                             y_var = "y",
                             outcome_predictive_vars = "outcome_pred_1")
# result summary
summary(results_ciprem)
# plot fitted results
plot(results_ciprem)

# PREMM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_premm <- Bayes_PREM(data = SimData_PREM,
                            id_var = "id",
                            time_var = "time",
                            y_var = "y",
                            n_class = 2)
# result summary
summary(results_premm)
# plot fitted results
plot(results_premm)


# CI-PREMM ---------------------------------------------------------------------------------
# fit Bayes_PREM()
results_cipremm <- Bayes_PREM(data = SimData_PREM,
                              id_var = "id",
                              time_var = "time",
                              y_var = "y",
                              n_class = 2,
                              class_predictive_vars = c("class_pred_1", "class_pred_2"),
                              outcome_predictive_vars = "outcome_pred_1")
# result summary
summary(results_cipremm)
# plot fitted results
plot(results_cipremm)

---

Extract class probabilities

Description

Extracts the posterior class probabilities for each individual from a fitted model of class "PREM".

Usage

getClassProb(x, ...)

## S3 method for class 'PREM'
getClassProb(x, ...)

## S3 method for class 'getClassProb.PREM'
print(x, ...)

Arguments

x	An object of class "PREM".
...	Additional arguments.

Value

Returns a list of the posterior class probabilities for each individual.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_prem)
# get class probabilities
getClassProb(results_prem)

---

Extract random coefficients

Description

Extracts the random coefficients from a fitted model of class "BPREM", "CREM", or "PREM".

Usage

getCoef(x, ...)

## S3 method for class 'BPREM'
getCoef(x, ...)

## S3 method for class 'CREM'
getCoef(x, ...)

## S3 method for class 'PREM'
getCoef(x, ...)

## S3 method for class 'getCoef'
print(x, ...)

Arguments

x	An object of class "BPREM", "CREM", or "PREM".
...	Additional arguments.

Value

Returns a data frame of the random coefficients for each individual/group.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_prem)
# get random coefficients
getCoef(results_prem)

---

Extract fitted values

Description

Extracts the individual fitted values from a fitted model of class "BPREM", "CREM", or "PREM".

Usage

getFitted(x, ...)

## S3 method for class 'BPREM'
getFitted(x, ...)

## S3 method for class 'CREM'
getFitted(x, ...)

## S3 method for class 'PREM'
getFitted(x, ...)

## S3 method for class 'getFitted'
print(x, ...)

Arguments

x	An object of class "BPREM", "CREM", or "PREM".
...	Additional arguments.

Value

Returns a data frame of the fitted values for each individual and timepoint.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_prem)
# get fitted values
getFitted(results_prem)

---

Extract fixed effects parameter estimates

Description

Extracts the fixed effects parameter estimates from a fitted model of class "BPREM", "CREM", or "PREM".

Usage

getFixEf(x, ...)

## S3 method for class 'BPREM'
getFixEf(x, ...)

## S3 method for class 'CREM'
getFixEf(x, ...)

## S3 method for class 'PREM'
getFixEf(x, ...)

## S3 method for class 'getFixEf'
print(x, ...)

Arguments

x	An object of class "BPREM", "CREM", or "PREM".
...	Additional arguments.

Value

Returns a vector or data frame of fixed effects parameter values.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_bprem)
# get fixed effects
getFixEf(results_bprem)

---

Extract changepoint probabilities

Description

Extracts the K (number of changepoints) probabilities from a fitted model of class "PREM".

Usage

getKProb(x, ...)

## S3 method for class 'PREM'
getKProb(x, ...)

## S3 method for class 'getKProb.PREM'
print(x, ...)

Arguments

x	An object of class "PREM".
...	Additional arguments.

Value

Returns a list of the posterior probabilities for each possible number of changepoints, for each class.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_prem)
# get changepoint probabilities
getKProb(results_prem)

---

Extract model fit

Description

Extracts the model fit information from a fitted model of class "BPREM", "CREM", or "PREM".

Usage

getModelFit(x, ...)

## S3 method for class 'BPREM'
getModelFit(x, ...)

## S3 method for class 'CREM'
getModelFit(x, ...)

## S3 method for class 'PREM'
getModelFit(x, ...)

## S3 method for class 'getModelFit'
print(x, ...)

Arguments

x	An object of class "BPREM", "CREM", or "PREM".
...	Additional arguments.

Value

Returns a vector of the model fit information (deviance, pD, DIC).

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_prem)
# get model fit
getModelFit(results_prem)

---

Extract random effects

Description

Extracts the random effects from a fitted model of class "BPREM" or "CREM".

Usage

getRanEf(x, ...)

## S3 method for class 'BPREM'
getRanEf(x, ...)

## S3 method for class 'CREM'
getRanEf(x, ...)

## S3 method for class 'getRanEf'
print(x, ...)

Arguments

x	An object of class "BPREM" or "CREM".
...	Additional arguments.

Value

Returns a list of the random effects for each individual/group.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_bprem)
# get random effects
getRanEf(results_bprem)

---

Extract random effects variance-covariance matrix

Description

Extracts the random effects variance-covariance matrix from a fitted model of class "BPREM", "CREM", or "PREM".

Usage

getVarCov(x, ...)

## S3 method for class 'BPREM'
getVarCov(x, ...)

## S3 method for class 'CREM'
getVarCov(x, ...)

## S3 method for class 'PREM'
getVarCov(x, ...)

## S3 method for class 'getVarCov.BPREM'
print(x, ...)

## S3 method for class 'getVarCov.CREM'
print(x, ...)

## S3 method for class 'getVarCov.PREM'
print(x, ...)

Arguments

x	An object of class "BPREM", "CREM", or "PREM".
...	Additional arguments.

Value

Returns a list of the random effects variance-covariance matrices.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_prem)
# get random effects variance-covariance matrices
getVarCov(results_prem)

---

Plot a BEND Model (PREM, CREM, BPREM)

Description

Generates a "spaghetti plot" of observed longitudinal trajectories for each individual. If the results from a BEND function are supplied, the trajectory defined by the mean parameters is shown in bold. If fitting a mixture (PREMM or CI-PREMM) or bivariate model (BPREM), the mean trajectories for classes or outcomes will be distinguished by color.

Usage

plot_BEND(
  data,
  id_var,
  time_var,
  y_var,
  y2_var = NULL,
  results = NULL,
  xlab = "X",
  ylab = "Y",
  colors = NULL,
  mean_colors = NULL,
  legend_pos = "topright",
  ...
)

Arguments

data	Data frame in long format, where each row describes a measurement occasion for a given individual. It is assumed that each individual has the same number of assigned timepoints (a.k.a., rows).
id_var	Name of column that contains ids for individuals with repeated measures in a longitudinal dataset.
time_var	Name of column that contains the time variable.
y_var	Name of column that contains the outcome variable.
y2_var	(for BPREM only) Name of column that contains the second outcome variable.
results	The output of BEND model to the data. If results=NULL, only a spaghetti plot of the data will be generated.
xlab	X-axis label for the generated plot.
ylab	Y-axis label for the generated plot.
colors	Colors for each class (PREMM or CI-PREMM) or outcome (BPREM). By default, up to 5 colors are provided in the following order: “blue” (class 1 and outcome 1), “red” (class 2 and outcome 2), “green” (class 3), “gold” (class 4), “gray” (class 5).
mean_colors	Colors for the trajectory defined by the mean parameters for each class (PREMM or CI-PREMM) or outcome (BPREM). By default, up to 5 colors are provided in the following order: “darkblue” (class 1 and outcome 1), “darkred” (class 2 and outcome 2), “darkgreen” (class 3), “gold4” (class 4), “darkgray” (class 5).
legend_pos	(optional) Option to change legend position (default = "topright").
...	(optional) Other parameters to pass to the plot() function.

Value

No return value, called to generate plot.

Author(s)

Corissa T. Rohloff

Examples

# load simulated data
data(SimData_PREM)
# plot observed data
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y")
# load fitted model results
data(results_prem)
# plot fitted results
plot_BEND(data = SimData_PREM,
          id_var = "id",
          time_var = "time",
          y_var = "y",
          results = results_prem)

---

Plot the results of a bivariate piecewise random effects model (BPREM)

Description

Provides a fitted plot of a BPREM model, as returned by Bayes_BPREM().

Usage

## S3 method for class 'BPREM'
plot(
  x,
  xlab = "X",
  ylab = "Y",
  colors = NULL,
  mean_colors = NULL,
  legend_pos = "topright",
  ...
)

Arguments

x	An object of class "BPREM" (returned by Bayes_BPREM(...)).
xlab	X-axis label for the generated plot.
ylab	Y-axis label for the generated plot.
colors	Colors for each class outcome. By default, up to 2 colors are provided in the following order: "blue" (outcome 1), "red" (outcome 2).
mean_colors	Colors for the trajectory defined by the mean parameters for each outcome. By default, up to 2 colors are provided in the following order: "darkblue" (outcome 1), "darkred" (outcome 2).
legend_pos	(optional) Option to change legend position (default = "topright").
...	(optional) Other parameters to pass to the plot() function.

Value

No return value.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_bprem)
# plot fitted results
plot(results_bprem)

---

Plot the results of a crossed random effects model (CREM)

Description

Provides a fitted plot of a CREM model, as returned by Bayes_CREM().

Usage

## S3 method for class 'CREM'
plot(
  x,
  xlab = "X",
  ylab = "Y",
  colors = NULL,
  mean_colors = NULL,
  legend_pos = "topright",
  ...
)

Arguments

x	An object of class "CREM" (returned by Bayes_CREM(...)).
xlab	X-axis label for the generated plot.
ylab	Y-axis label for the generated plot.
colors	Color for observed trajectories (optional). Default is "grey".
mean_colors	Colors for the trajectory defined by the mean parameters for each outcome (optional). Default is "black".
legend_pos	(optional) Option to change legend position (default = "topright").
...	(optional) Other parameters to pass to the plot() function.

Value

No return value.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_pcrem)
# plot fitted results
plot(results_pcrem)

---

Plot the results of a piecewise random effects model (PREM)

Description

Provides a fitted plot of a PREM model, as returned by Bayes_PREM().

Usage

## S3 method for class 'PREM'
plot(
  x,
  xlab = "X",
  ylab = "Y",
  colors = NULL,
  mean_colors = NULL,
  legend_pos = "topright",
  ...
)

Arguments

x	An object of class "PREM" (returned by Bayes_PREM(...)).
xlab	X-axis label for the generated plot.
ylab	Y-axis label for the generated plot.
colors	Colors for each class (PREMM or CI-PREMM). By default, up to 5 colors are provided in the following order: "blue" (class 1), "red" (class 2), "green" (class 3), "gold" (class 4), "gray" (class 5).
mean_colors	Colors for the trajectory defined by the mean parameters for each class (PREMM or CI-PREMM). By default, up to 5 colors are provided in the following order: "darkblue" (class 1), "darkred" (class 2), "darkgreen" (class 3), "gold4" (class 4), "darkgray" (class 5).
legend_pos	(optional) Option to change legend position (default = "topright").
...	(optional) Other parameters to pass to the plot() function.

Value

No return value.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_prem)
# plot fitted results
plot(results_prem)

---

Print the results of a bivariate piecewise random effects model (BPREM)

Description

Provides a summary of a BPREM model, as returned by Bayes_BPREM().

Usage

## S3 method for class 'BPREM'
print(x, ...)

Arguments

x	An object of class "BPREM" (returned by Bayes_BPREM(...)).
...	Additional arguments.

Value

Returns a list of key parameter estimates.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_bprem)
# print results
print(results_bprem)

---

Print the results of a crossed random effects model (CREM)

Description

Provides a summary of a CREM model, as returned by Bayes_CREM().

Usage

## S3 method for class 'CREM'
print(x, ...)

Arguments

x	An object of class "CREM" (returned by Bayes_CREM(...)).
...	Additional arguments.

Value

Returns a list of key parameter estimates.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_pcrem)
# print results
print(results_pcrem)

---

Print the results of a piecewise random effects model (PREM)

Description

Provides a summary of a PREM model, as returned by Bayes_PREM().

Usage

## S3 method for class 'PREM'
print(x, ...)

Arguments

x	An object of class "PREM" (returned by Bayes_PREM(...)).
...	Additional arguments.

Value

Returns a list of key parameter estimates.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_prem)
# print results
print(results_prem)

---

Fitted results for a BPREM

Description

Simulated data for a bivariate piecewise random effects model (BPREM) using SimData_BPREM. Included to demonstrate the use of summary.BPREM().

Results from fitting a bivariate piecewise random effects model (BPREM) to SimData_BPREM (returned by Bayes_BPREM(...)).

Usage

data(results_bprem)

results_bprem

Format

A list (an object of class BPREM) with fitted model results.

results_bprem

A list object with elements:

Call

Function arguments

Sample_Size

Data set sample size

Data

Data used for model fitting

Convergence

Convergence status

Model_Fit

Model fit information

Fitted_Values

Fitted outcome values

Parameter_Estimates

Parameter estimates

Random_Coefficients

Random coefficient estimates

Run_Time

Model run time

---

Fitted results for a PCREM

Description

Simulated data for a piecewise crossed random effects model (PCREM) using SimData_CREM. Included to demonstrate the use of summary.CREM().

Results from fitting a piecewise crossed random effects model (PCREM) to SimData_PCREM (returned by Bayes_CREM(...)).

Usage

data(results_pcrem)

results_pcrem

Format

A list (an object of class CREM) with fitted model results.

results_pcrem

A list object with elements:

Call

Function arguments

Sample_Size

Data set sample size

Data

Data used for model fitting

Convergence

Convergence status

Model_Fit

Model fit information

Fitted_Values

Fitted outcome values

Parameter_Estimates

Parameter estimates

Random_Coefficients

Random coefficient estimates

Run_Time

Model run time

---

Fitted results for a PREM

Description

Fitted results for a piecewise random effects model (PREM) using SimData_PREM. Included to demonstrate the use of plot_BEND() and summary.PREM().

Results from fitting a piecewise random effects model (PREM) to SimData_PREM (returned by Bayes_PREM(...)).

Usage

data(results_prem)

results_prem

Format

A list (an object of class PREM) with fitted model results.

results_prem

A list object with elements:

Call

Function arguments

Sample_Size

Data set sample size

Data

Data used for model fitting

Convergence

Convergence status

Model_Fit

Model fit information

Fitted_Values

Fitted outcome values

Parameter_Estimates

Parameter estimates

Random_Coefficients

Random coefficient estimates

Run_Time

Model run time

---

Simulated data for a BPREM

Description

Simulated data for a bivariate piecewise random effects model (BPREM) with 7 timepoints collected on 30 individuals.

A simulated dataset for the bivariate piecewise random effects model (BPREM).

Usage

data(SimData_BPREM)

SimData_BPREM

Format

A data frame with 210 rows and 4 variables.

SimData_BPREM

A data frame with 210 rows and 4 columns:

id

Individual ids

time

Time

y1

Outcome 1

y2

Outcome 2

Details

• id ID for each individual.

• time Timepoints for each individual.

• y1 Outcome 1.

• y2 Outcome 2.

---

Simulated data for a PCREM

Description

Simulated data for a piecewise crossed random effects model (PCREM) with 7 timepoints collected on 30 individuals.

A simulated dataset for the piecewise crossed random effects model (PCREM).

Usage

data(SimData_PCREM)

SimData_PCREM

Format

A data frame with 210 rows and 4 variables.

SimData_PCREM

A data frame with 210 rows and 4 columns:

id

Individual ids

teacherid

Teacher ids

time

Time

y

Outcome

Details

• id ID for each individual.

• teacherid ID for each teacher.

• time Timepoints for each individual.

• y Outcome.

---

Simulated data for a PREM + Extensions

Description

Simulated data for a piecewise random effects model (PREM) and useful extensions (CI-PREM, PREMM, CI-PREMM) with 18 timepoints collected on 30 individuals.

A simulated dataset for the piecewise random effects model (PREM).

Usage

data(SimData_PREM)

SimData_PREM

Format

A data frame with 540 rows and 6 variables.

SimData_PREM

A data frame with 540 rows and 6 columns:

id

Individual ids

time

Time

y

Outcome

class_pred_1

First Class-Predictive Covariate

class_pred_2

Second Class-Predictive Covariate

outcome_pred_1

First Outcome-Predictive Covariate

Details

• id ID for each individual.

• time Timepoints for each individual.

• y Outcome.

• class_pred_1 First class predictive covariate (time-invariant).

• class_pred_2 Second class predictive covariate (time-invariant).

• outcome_pred_1 Outcome predictive covariate (time-varying).

---

Summarize the results of a bivariate piecewise random effects model (BPREM)

Description

Provides a summary of a BPREM model, as returned by Bayes_BPREM().

Usage

## S3 method for class 'BPREM'
summary(object, ...)

## S3 method for class 'summary.BPREM'
print(x, ...)

Arguments

object	An object of class "BPREM" (returned by Bayes_BPREM(...)).
...	Additional arguments.
x	An object of class "summary.BPREM".

Value

Returns a list of key parameter estimates.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_bprem)
# result summary
summary(results_bprem)

---

Summarize the results of a crossed random effects model (CREM)

Description

Provides a summary of a CREM model, as returned by Bayes_CREM().

Usage

## S3 method for class 'CREM'
summary(object, ...)

## S3 method for class 'summary.CREM'
print(x, ...)

Arguments

object	An object of class "CREM" (returned by Bayes_CREM(...)).
...	Additional arguments.
x	An object of class "summary.CREM".

Value

Returns a list of key parameter estimates.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_pcrem)
# result summary
summary(results_pcrem)

---

Summarize the results of a piecewise random effects model (PREM)

Description

Provides a summary of a PREM model, as returned by Bayes_PREM().

Usage

## S3 method for class 'PREM'
summary(object, ...)

## S3 method for class 'summary.PREM'
print(x, ...)

Arguments

object	An object of class "PREM" (returned by Bayes_PREM(...)).
...	Additional arguments.
x	An object of class "summary.PREM".

Value

Returns a list of key parameter estimates.

Author(s)

Corissa T. Rohloff

Examples

# load fitted model results
data(results_prem)
# result summary
summary(results_prem)

---